what happens when the laws of nature break down as they do in black holes?

That's not technically correct. The mathematics break down.

A distinction without a difference

I disagree. The laws of nature don't break down. Our understanding of the laws of nature is limited and breaks down. The math does not exist to properly model what happens at the singularity because our understanding of the physics is incomplete when the size of the universe is infinitesimally small.

So you said thing like math are discovered so that mathematics must exist outside the human brain now you say that math to describe what happens in black holes doesn't exist.

So which is it?

OR

Maybe the minds of human beings are incapable of the intellectual processes needed to understand what happens in the instances where math fails.

It is neither. Our understanding of the physics is limited. Because our understanding of the physics is incomplete, the equations - or math - is limited. Therefore, the equations - or math - do not presently exist to describe what happens when the field equations yield infinite densities.

The math is not failing. The math is showing the limitation or boundary of our understanding of the physics.

So now you say we have to create the math that is needed to understand these things. But earlier you said mathematics wasn't created by humans but was "discovered" because it already existed before humans did.

So which is it?

Neither because you keep misstating what I write. Try using my exact quote to make your points and you will discover your error.

You said math was discovered not created by humans.

That means mathematics exist apart from humans and the human brain.

Then you say that no math exists to describe what happens in black holes but you imply that it must exist because humans did not create mathematics but rather discovered it.

So how can you say that the math to describe black holes doesn't exist?

It does not imply that at all. The physics have not been discovered that describe what happens when Friedmann's solution to Einstein's field equations yield infinite densities. Once the physics are discovered it can be modeled using mathematical equations.

Of course it does

Either man invented the concepts of mathematics or man didn't.

You said man discovered them that means that mathematics exist whether or not humans exist.

You are all over the map. Man discovered the concepts of math. Math is not unique to man. Any intelligent being can discover the concepts of math. Mathematical truths exist independent of any creature. Mathematical truths exist in and of themselves.

Just as man did not invent that water consists of two hydrogen atoms and one oxygen atom. Man discovered that water consists of two hydrogen atoms and one oxygen atom.

So then how can you say the math to describe black holes doesn't exist?

Again... not that they don't exist but that the present equations yield infinite densities at it's boundary. You keep misstating that. But to answer your question the math hasn't been discovered yet because the physics of the boundary condition has not been discovered yet.

So now you are saying that the math does exist?

Make up your mind.

If the math does exist then we must be incapable of understanding it.

The math that describes what happens at the boundary of black holes or the beginning of the universe has not been discovered yet because the physics for those events has not been discovered yet.

So now you are saying that those things exist out there in the ether somewhere and we will eventually stumble upon them.

That is not the same thing as saying they do not exist.

See the 2 min 35 sec mark.

So he's saying that the math exists you are saying it doesn't exist.

And that is just one man's opinion anyway.

We are both saying that mathematical and scientific truths are discovered. Just like logic is discovered. No one invented that if A=B and B=C then A must equal C. Just like no one invented A^2 + B^2 = C^2 for right triangles. These truths were discovered.

But please do keep arguing against it. I can do this all day.

So you're changing your tune again.

Did you not say the math does not exist?

If it does not exist it cannot be discovered can it?

Exact right triangles are a man made construct. So the math describing them is a man made construct

There is no reason to think the mathematics of an alien intelligence will be the same as ours.